Of the uninsured, six in 10, or 62 percent, are Hispanic, and 29 percent are "unable to take advantage of coverage expansions under the ACA due to their immigration status," the survey says. Around four in 10, or 39 percent, of those ineligible due to immigration status "have incomes that put them in the group likely eligible for Medi-Cal and another quarter (24 percent) are likely eligible for financial assistance through Covered California," according to the survey. Seventy percent of the uninsured Hispanics prefer to speak in Spanish.

"They've always been a majority of the uninsured [in California]," Mollyann Brodie, overseer of Kaiser Family Foundation's public opinion surveys, told CNBC.

In addition, almost four in 10, or 37 percent, of the insured have never had health insurance, and 45 percent have not have insurance for at least two years.

"It shows that the work just gets harder from here because the uninsured who remain are people who have been uninsured for a very long time and are populations that will be more difficult to reach, including Latinos," Drew Altman, president and chief executive of Kaiser Family Foundation, said according to The Associated Press.

Last year, Covered California, California's government exchange for purchasing insurance plans by private companies, was criticized for not reaching out to the Hispanic community and having a faulty Spanish-language website. James Scullary told AP that Covered California is "doubling down on our enrollment activities" in 2014. This includes allotting $168 million to outreach programs for three months starting in November, which is more money than the agency spent during six months in 2013. In addition, Covered California will hire more bilingual call center workers.

Scullary said that the agency has extended outreach and marketing toward Hispanics. As a result, final enrollment reached 305,106, topping projections of 265,000.

"I have been very much involved in ensuring that this very hard-to-reach population is able to have the same opportunities that everyone else has had to enroll or purchase a product that they absolutely need," Sen. Norma Torres, D-Pomona, who wrote a bill encouraging exchange board diversity to encourage minority enrollment, said.